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Simplifying d2 + -14d + 49 = 10 Reorder the terms: 49 + -14d + d2 = 10 Solving 49 + -14d + d2 = 10 Solving for variable 'd'. Reorder the terms: 49 + -10 + -14d + d2 = 10 + -10 Combine like terms: 49 + -10 = 39 39 + -14d + d2 = 10 + -10 Combine like terms: 10 + -10 = 0 39 + -14d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + -14d + -39 + d2 = 0 + -39 Reorder the terms: 39 + -39 + -14d + d2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -14d + d2 = 0 + -39 -14d + d2 = 0 + -39 Combine like terms: 0 + -39 = -39 -14d + d2 = -39 The d term is -14d. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14d + 49 + d2 = -39 + 49 Reorder the terms: 49 + -14d + d2 = -39 + 49 Combine like terms: -39 + 49 = 10 49 + -14d + d2 = 10 Factor a perfect square on the left side: (d + -7)(d + -7) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (d + -7) equal to 3.16227766 and -3.16227766.Subproblem 1
d + -7 = 3.16227766 Simplifying d + -7 = 3.16227766 Reorder the terms: -7 + d = 3.16227766 Solving -7 + d = 3.16227766 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + d = 3.16227766 + 7 Combine like terms: -7 + 7 = 0 0 + d = 3.16227766 + 7 d = 3.16227766 + 7 Combine like terms: 3.16227766 + 7 = 10.16227766 d = 10.16227766 Simplifying d = 10.16227766Subproblem 2
d + -7 = -3.16227766 Simplifying d + -7 = -3.16227766 Reorder the terms: -7 + d = -3.16227766 Solving -7 + d = -3.16227766 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + d = -3.16227766 + 7 Combine like terms: -7 + 7 = 0 0 + d = -3.16227766 + 7 d = -3.16227766 + 7 Combine like terms: -3.16227766 + 7 = 3.83772234 d = 3.83772234 Simplifying d = 3.83772234Solution
The solution to the problem is based on the solutions from the subproblems. d = {10.16227766, 3.83772234}
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